Jon Kleinberg, a computer scientist at Cornell, and Lars Backstrom, a senior engineer at Facebook, took a dataset of 1.3 million Facebook users who listed that they were in a relationship. They were actually looking for a formula that could predict which users were in relationships with each other.

They found that the shape, or "dispersion," of your friends network is the key. You might expect that a cluster of mutual friends indicates two people are in a relationship but the opposite is the case: You're more likely to have cluster of mutual coworkers listing each other as friends than a couple.

Instead, when two people have widely dispersed clusters that are linked mostly via the couple, that is the main predictor of whether you're in a relationship. Here's what it looks like:

In this diagram, "you" are at the center. The two dense clusters of friends are coworkers and college friends. The blue dot in the lower left is the significant other — he or she is at a remove from most of your friends but has links to many of them.

The dispersion formula makes it easier to guess who is in a relationship with whom.

But when the formula guesses incorrectly, that means a couple is more likely to break up soon, the researchers say:

We find that relationships on which recursive dispersion fails to correctly identify the partner are significantly more likely to transition to ‘single’ status over a 60- day period. This effect holds across all relationship ages and is particularly pronounced for relationships up to 12 months in age; here the transition probability is roughly 50% greater when recursive dispersion fails to recognize the partner.

The red line shows incorrect guesses by the formula. When it fails to spot a couple based on dispersion, that couple has a much higher likelihood of breaking up within the next five months, the data suggest.